Abstract
In this chapter, we discuss the local ABCs for the exterior problem of 2-D and 3-D Poisson equations, and for the wave equations on unbounded domains. By using artificial boundaries, the original problems are reduced to boundary or initial boundary value problems on bounded computational domains. Local boundary conditions on the artificial boundaries are obtained. Some error estimates are also given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alpert, B., Greengard, L. and Hagstrom, T. (2002), Nonreflecting boundary conditions for the time-dependent wave equations, J. Comput. Phys., 180(2002), 270–296.
Bao, W.Z. and Han, H.D. (1997), Local artificial boundary conditions for the incompressible viscous flow in a slip channel, J. Comp. Math., 15(1997), 335–343.
Bao, W.Z. and Han, H.D. (2000), High-order local artificial boundary conditions for problems in unbounded domains, Comput. Methods Appl. Mech. Engrg., 188 (2000), 455–471.
Collino, F. (1993). High order absorbing boundary conditions for wave propagation models. Straight line boundary and corner cases, in: R. Kleinman, et al. (Eds.), Proceedings of the Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, SIAM, Delaware, 1993, pp. 161–171.
Engquist, B. and Majda, A. (1977), Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977), 629–651.
Givoli, D. (2004), High order local non-reflecting boundary conditions: a review, Wave Motion, 39(2004), 319–326.
Givoli, D. and Keller, J.B. (1994), Special finite elements for use with highorder boundary conditions, Comp. Meth. Appl. Mech. Engrg., 119(1994), 199–213.
Han, H.D. and Wu, X.N. (1985-A), Approximation of infinite boundary condition and its application to finite element methods, J. Comp. Math., 3(1985), 179–192.
Han, H.D. and Zheng, C.X. (1999), High-order local artificial boundary conditions of the exterior problem of Poisson equations in 3-D space, Numer. Math. (a journal of chinese universities), 23(1999), 290–304.
Han, H.D. and Zheng, C.X. (2002-A), Mixed Finite Element Method and Higher-order Local artificial boundary conditions for exterior 3-D Poisson equation, Tsinghua Science and Technology, 7 (2002), 228–234.
Han, H.D. and Zheng, C.X. (2002-B), Mixed finite element and high-order local artificial boundary conditions of elliptic equation, Comp. Meth. Appl. Mech. Engrg., 191 (2002), 2011–2027.
Oleinik, O.A. (1987), On the behavior at infinity of solutions of second order elliptic equations, In Ordinary and Partial Differential Equations. (Dundee, 1986), Pitman Res. Notes Math. Ser. 157, Longman Sci. Tech., Harlow.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Han, H., Wu, X. (2013). Local Artificial Boundary Conditions. In: Artificial Boundary Method. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35464-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-35464-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35463-2
Online ISBN: 978-3-642-35464-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)